1. Preheat oven to 350° F.
2. Beat together butter, coconut oil and sugar in a stand mixer until pale and fluffy (this should take about 10 minutes, you want it really fluffy). Once it's nice and fluffy, beat in the vanilla.
3. With mixer on low, gradually add flour and 1/2 teaspoon table salt. Mix until combine.
4. Press dough together and roll into 1 1/4-inch balls. Dip each ball into the beaten eggs, and roll in coconut.
5. On a parchment-lined baking sheet arrange prepared balls and press an indentation into each using your thumb.
6. Bake for 10 minutes, remove baking sheets from oven and re-press indentations if needed. Bake cookies until golden, 9 to 10 minutes more and allow to cool on wire racks. While the cookies are cooling, prepare the salted caramel filling.
7. In a small saucepan bring the sugar and water to a boil, swirling from time to time until a nice golden brown color is achieved, this should take about 8 minutes. Remove from heat and add cream and butter. Bring the mixture back to a boil and continue to cook until all ingredients are incorporated. Stir in salt and allow to cool slightly.
8. Using a spoon, fill the thumbprints with the warm caramel. Once the caramel has cooled and set add flaky salt and serve.

*This recipe was adapted from Martha Stewart.